R. Abraham, J. E. Marsden, and T. S. Ratiu, Manifolds, tensor analysis , and applications, Applied Mathematical Sciences, vol.75, 1988.
DOI : 10.1007/978-1-4612-1029-0

F. Michael and . Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc, vol.14, issue.1, pp.1-15, 1982.

H. Biller, Characterizations of proper actions, Mathematical Proceedings of the Cambridge Philosophical Society, vol.136, issue.2, pp.429-439, 2004.
DOI : 10.1017/S0305004103007217

A. D. Blaom, A geometric setting for Hamiltonian perturbation theory, Memoirs of the American Mathematical Society, vol.153, issue.727, p.112, 2001.
DOI : 10.1090/memo/0727

E. David and . Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics. Birkhäuser Boston Inc, vol.203, 2002.

C. Balleier and T. Wurzbacher, On the geometric quantization of symplectic Howe pairs, 2009.

J. Johannes, J. A. Duistermaat, and . Kolk, Lie groups. Universitext, 2000.

J. J. Duistermaat, The heat kernel Lefschetz fixed point formula for the spin c Dirac operator, Progress in Nonlinear Differential Equations and their Applications, 1996.

S. Victor-guillemin and . Sternberg, Geometric quantization and multiplicities of group representations, Inventiones Mathematicae, vol.30, issue.35, pp.515-538, 1982.
DOI : 10.1007/978-3-662-00095-3

S. Victor-guillemin and . Sternberg, Symplectic techniques in physics, 1990.

R. Goodman and N. R. Wallach, Representations and invariants of the classical groups, volume 68 of Encyclopedia of Mathematics and its Applications, 1998.

S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol.34, 1978.
DOI : 10.1090/gsm/034

J. Hilgert, K. Neeb, and W. Plank, Symplectic convexity theorems and coadjoint orbits, Compositio Math, vol.94, issue.2, pp.129-180, 1994.

R. Howe, Dual pairs in physics: harmonic oscillators, photons, electrons, and singletons. In Applications of group theory in physics and mathematical physics, Lectures in Appl. Math, vol.21, pp.179-207, 1982.

R. Howe, Remarks on classical invariant theory, Transactions of the American Mathematical Society, vol.313, issue.2, pp.539-570, 1989.
DOI : 10.1090/S0002-9947-1989-0986027-X

A. T. Huckleberry and T. Wurzbacher, Multiplicity-free complex manifolds, Mathematische Annalen, vol.218, issue.1-3, pp.261-280, 1990.
DOI : 10.1007/BF01370814

Y. Karshon and E. Lerman, The centralizer of invariant functions and division properties of the moment map, Illinois J. Math, vol.41, issue.3, pp.462-487, 1997.

B. Kostant, Quantization and unitary representations, Lecture Notes in Math, vol.76, pp.87-208, 1970.
DOI : 10.2307/2372397

J. Ortega and T. S. Ratiu, Momentum maps and Hamiltonian reduction, Progress in Mathematics Birkhäuser Boston Inc, vol.222, 2004.
DOI : 10.1007/978-1-4757-3811-7

R. S. Palais, On the Existence of Slices for Actions of Non-Compact Lie Groups, The Annals of Mathematics, vol.73, issue.2
DOI : 10.2307/1970335

M. J. Pflaum, Analytic and geometric study of stratified spaces, Lecture Notes in Mathematics, vol.1768, 2001.

C. Procesi, Lie groups. Universitext An approach through invariants and representations, 2007.

H. Rubenthaler, Les paires duales dans les algèbres de Lie réductives, Astérisque, issue.219, p.121, 1994.

G. W. Schwarz, Smooth functions invariant under the action of a compact lie group, Topology, vol.14, issue.1, pp.63-68, 1975.
DOI : 10.1016/0040-9383(75)90036-1

M. Schmidt, Classification and partial ordering of reductive Howe dual pairs of classical Lie groups, Journal of Geometry and Physics, vol.29, issue.4, pp.283-318, 1999.
DOI : 10.1016/S0393-0440(98)00043-6

R. Mark and . Sepanski, Compact Lie groups, Graduate Texts in Mathematics, vol.235, 2007.

R. Sjamaar, Holomorphic Slices, Symplectic Reduction and Multiplicities of Representations, The Annals of Mathematics, vol.141, issue.1, pp.87-129, 1995.
DOI : 10.2307/2118628

[. Sjamaar, Convexity Properties of the Moment Mapping Re-examined, Advances in Mathematics, vol.138, issue.1, pp.46-91, 1998.
DOI : 10.1006/aima.1998.1739

H. Joseph, G. Sampson, and . Washnitzer, A Künneth formula for coherent algebraic sheaves, Illinois J. Math, vol.3, pp.389-402, 1959.

S. Veeravalli and . Varadarajan, Harmonic analysis on real reductive groups, Lecture Notes in Mathematics, vol.576, 1977.

. Außerdem-nehmen-wir-an, dass ein Punkt z 0 ? ? existiert, in dem g 1 · z 0 = (g 2 · z 0 ) ? gilt Dann: (i) ?z ? ? : g 1 · z = (g 2 · z) ? , (ii) ?z ? ? : ? ?1 i (? i (z))

D. Literatur-références-literatur-anthony and . Blaom, A geometric setting for Hamiltonian perturbation theory

A. T. Huckleberry and T. Wurzbacher, Multiplicity-free complex manifolds, Mathematische Annalen, vol.218, issue.1-3, pp.261-280, 1990.
DOI : 10.1007/BF01370814

Y. Karshon and E. Lerman, The centralizer of invariant functions and division properties of the moment map, Illinois J. Math, vol.41, issue.3, pp.462-487, 1997.

B. Kostant, Quantization and unitary representations, Lecture Notes in Math, vol.76, pp.87-208, 1970.
DOI : 10.2307/2372397

M. Molitor, Grassmanniennes non-linéaires, groupes de difféomorphismes unimodulaires et quelqueséquationsquelqueséquations hamiltoniennes en dimension infinie, 2007.

J. Ortega and T. S. Ratiu, Momentum maps and Hamiltonian reduction, Progress in Mathematics Birkhäuser Boston Inc, vol.222, 2004.
DOI : 10.1007/978-1-4757-3811-7

R. Sjamaar, Holomorphic Slices, Symplectic Reduction and Multiplicities of Representations, The Annals of Mathematics, vol.141, issue.1, pp.87-129, 1995.
DOI : 10.2307/2118628

H. Joseph, G. Sampson, and . Washnitzer, A Künneth formula for coherent algebraic sheaves, Illinois J. Math, vol.3, pp.389-402, 1959.